Francisca Silva

Title

Sets as rigid embodiments of materially equivalent rigid embodiments

Abstract

Albeit having some initial plausibility, most philosophers today would reject the thesis that members of sets are parts of sets, instead following Lewis (1991, 1993) in taking sets and classes more generally to have only their subclasses as parts, with singletons being mereologically atomic. Against this background, Caplan et. al (2010) attempt to maintain that sets have their members as parts, within the framework of Fine's (1999, 2010) theory of rigid embodiments. According to them, sets just are rigid embodiments having as a formal part having some attribute or another. Their view, however, is committed to a rejection of classical mereology as it very directly entails failures of the principle of strong supplementation. In this talk I will attempt to motivate a (work-in-progress) view of the mereology of sets based on Fine's theory of rigid embodiments in which: (i) the members of sets are parts of sets; and (ii) no principle of classical mereology is violated. The resulting view is that sets just are rigid embodiments having as a formal part the group property being unified and as material parts rigid embodiments sharing the same material parts. According to this view of sets, to construct, for instance, the set {Lewis, Fine} one would first take all the rigid embodiments having both Fine and Lewis as material parts and nothing else, and would then form a rigid embodiment out of all of them with the help of the predicate being unified.

Date / Time / Place

June 23rd / 11:35 / Aula 0A